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Fixed Effects Estimation of Structural Parameters and Marginal Effects in Panel Probit Models



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Fixed Effects Estimation of Structural Parameters and Marginal Effects in Panel Probit Models Iva n Ferna ndez Val Department of Economics Boston University February 10 2007 Abstract Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem In this paper I find that the most important component of this incidental parameters bias for probit fixed effects estimators of index coefficients is proportional to the true value of these coefficients using a large T expansion of the bias This result allows me to derive a lower bound for this bias and to show that fixed effects estimates of ratios of coefficients and average marginal effects have zero bias in the absence of heterogeneity and have negligible bias relative to their true values for a wide variety of distributions of regressors and individual effects New bias corrected estimators for index coefficients and marginal effects with improved finite sample properties are also proposed for static and dynamic probit logit and linear probability models with predetermined regressors JEL Classification C23 C25 J22 Keywords Panel data Bias Discrete Choice Models Probit Fixed effects Labor Force Participation Acknowledgment I wish to thank Josh Angrist Victor Chernozhukov and Whitney Newey for encouragement and advice I thank Jesu s Carro for sharing his data For suggestions and comments I am grateful to Paula Bustos Sylvain Chassang Michael Jansson Guido Kuersteiner Arthur Lewbel and the seminar participants at MIT Chicago GSB UBC Harvard KSG Boston University Universidad de Navarra LSE CEMFI UAB UPF Banco de Espan a University of Chicago Brown University Princeton University and 2006 Winter Econometric Society Meetings All remaining errors are mine I gratefully acknowledge financial support from Fundacio n Caja Madrid and Fundacio n Ramo n Areces Please send comments or suggestions to ivanf bu edu 1 Introduction Panel data models are widely used in empirical economics



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